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In a certain clothing store 6 shirts and 3 ties cost $79.50 and 3 shirts and 2 ties cost $41 determine the cost of each shirt

User Jawr
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1 Answer

14 votes
14 votes

9514 1404 393

Answer:

$12 for each shirt

Explanation:

If we let 's' and 't' represent the costs of a shirt and tie, respectively, then we can write the general form equations ...

6s +3t -79.50 = 0

3s +2t -41.00 = 0

The solution for s can be found using the "cross multiplication" technique.

Differences of products can be formed:

d1 = (6)(2) -(3)(3) = 3

d2 = (3)(-41) -(2)(-79.50) = 36

Then we have ...

1/d1 = s/d2 ⇒ s = d2/d1 = 36/3 = 12

The cost of each shirt is $12.00.

___

2 ties cost 41-36 = 5, so each one is $2.50.

_____

Additional comment

The use of simple elimination on this set of equations would eliminate the s-variable, so would mean additional work to find s after finding t. The t-variable could be eliminated by multiplying one equation by one coefficient, and the other by a different coefficient. As long as we're doing that amount of work, we may as well do just enough cross-multiplication to get the one answer we need. This is where the "cross-multiplication" method of solution comes in handy.

This method solves the general-form equations ...

  • ax +by +c = 0
  • dx +ey +g = 0

by considering the two rows of coefficients:

  • a, b, c, a
  • d, e, g, d

Then differences of cross-products are formed in adjacent columns:

d1 = ae -db

d2 = bg -ec

d3 = cd -ga

The solutions are ...

1/d1 = x/d2 = y/d3 ⇒ x = d2/d1, y = d3/d1

User Delbertooo
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